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rBri4R^CO7I1PACTUS.
AMR PUBLICATIONS COMPACTUS(LENDING SECTION)
DEPARTMENT OFNATIONAL RESOURCES
NATIONAL DEVELOPMENT
•BUREAU OF MINERAL RESOURCES,GEOLOGY AND GEOPHYSICS•
Record 1979/29
GRAV3 : AN INTERACTIVE COMPUTER PROGRAM TO CALCULATE
THE GRAVITY ANOMALY OF A FINITE HORIZONTAL PRISM
by
R.D. Ogilvy
The information contained in this report has been obtained by the Department of National Resourcesas part of the policy of the Australian Government to assist in the exploration and development of- -I resources. it may not be published in any form or used in a company prospectus or statement
the permission in writing of the Director. Bureau of Mineral Resources, Geology and Geophysics.
BMRRecord1[9/7-0,749
fi.‘
_
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Record 1979/29
GRAV3 •: AN INTERACTIVE COMPUTER PROGRAM TO CALCULATE
THE GRAVITY ANOMALY OF A FINITE HORIZONTAL PRISM
•^ by
0^ R.D. Ogilvy
•
•
•
CONTENTS
Page
SUMMARY
1. INTRODUCTION^ 1
2. CO—ORDINATE SYSTEM AND FORMULAE^ 2
3. PROGRAM DESCRIPTION^ 4
Flow chart^ 4•
Data input^ 4
Loading the program^ 5
Running the program^ 5
Data output^ 6
4. PROGRAM TESTING^ 6
5. EXAMPLES^ 7
6. REFERENCES^ 7
APPENDIX : Program listing
ILLUSTRATIONS
Figure. 1
Figure 2
Figure.3
Figure 4
Figure 5
Co—ordinate system and notations
Program flow chart
Teletype input/output
Program testing
Examples
SUMMARY
A description is given of a cavputer_program
• (GRAV3) used for calculating the gravity anomaly due to a
finite prism. The program is written in FORTRAN IV for
interactive use with an HP 21MX mini-computer and GOULD 5000
printer/plotter under RTE II using TEROS.
The program may be compiled, loaded, and executed
using a system teletype.^Little or no data preparation is
required and interpretation is achieved by forward
interactive modelling.
The program provides a computer plot together with
suitable annotation and a cross-section of the case
• modelled.
1.^INTRODUCTION
In metalliferous-exploration the need commonly
• arises to interpret gravity anomalies which are caused by
tabular bodies of finite strike length. The horizontal
prism of trapezium cross-section provides the interpreter
with a simple yet realistic geometrical form for a first-
order interpretation of an anomaly.
A computer program is described for calculating
the gravity anomaly of a finite homogeneous horizontal
prism. The program is called GRAV3 and is based on formulae
derived by Hjelt (1974).
The program has been written in FORTRAN IV for
interactive use with an HP 21MX mini-computer and a GOULD
5000 printer/plotter under RTE II using TEROS., The basic
program algorithm is simple and rapid, and could be readily
adapted for use with some of the more recent desk top
• calculators.^Little or no data preparation is required,
and interpretation is achieved by forward interactive
modelling.
•
•
•
•
2.
2. CO-ORDINATE SYSTEM AND FORMULAE
Co-ordinate system
A rectangular co-ordinate system is used (Fig.1)
with the X axis perpendicular to the strike direction, the Y
axis parallel to the strike, and the Z axis positive
downwards. The dipping surfaces of the prism are defined
by the angles c and G. A special case of the model is
that of a prism in which C^e . The top and bottom faces
of the structure are horizontal, and the two faces
perpendicular to the strike direction are vertical.
The corners of the prism are defined by their
X,Y,Z co-ordinates (e.g. Xl, Yi, z1) and the distances
between the prism and the observation point P(X, Y, Z) are
denoted by U, V, and W as shown in Figure 1.
Oblique profiles
Profiles, other than those normal to the prism
strike, can be run by defining a profile co-ordinate system,
at an angle a to the prism co-ordinate system (see Fig.lb). In such cases, program GRAV3 plots the calculated
gravity values with respect to the profile co-ordinate
system.
•
0^XI^X2 0
W(2)1Zl .10
( XV I, Z l,)YI w(i)
Z2U( l)
IV(2) 1.) (x,y,z,)1
3̂.4V(I)
U(2)'
U(I)4 3̂.1
U(2)
Y2
Plan Cross - section
a) Horizontal prism
0YN
b) Oblique profile
Plan
Fig. I Co—ordinate system and notations
Record No /979/29 G29- 263A
•^ 3.
Mathematical formulae
The gravity anomaly of a finite dipping prism (8 = E) is
given by Hjelt (1974):
•^Ag = G.Ap.To
where^Ap is the density contrast, G the gravitational constant, and
•^ U V W
^
1^1^1To =[[( (0^+0+0+0+0))^)^)
1^2^3^4^5
^
U^V^W
^
2^2^2
where(UV)
0^= W arctan1^WR
0^= -p. sin^E cos E arctan^(V.q) 2
• p.R
20^= -p. sin^E^tn (V + R)3
T^= -V.^tn (U + R)4
0^=^V. cos^E^tn (q. sin E + R)5
R =^NA2 +V +W 2
p = U - W cot E•^q = W + U cot E
The gravity anomaly of a prism with a more general•^trapezium cross-section is obtained by substituting 8 for E1
when U = U(2)or u(2) (see Fig. 1)
•
4.
3.^PROGRAM DESCRIPTION
Flow chart
The essential elements of the program structure are shown
in the flow chart (Fig. 2)r .^Program variables used in the flow
chart are defined in the program listing (see Appendix). For
operational convenience in BMR, a number of system subroutines are
used, but these do not detract from the generality of the basic
program algorithm. System subroutines are referred to by name
(e.g. RMPAR, NUMB, etc.) and further details may be obtained from
the HP-RTE II system manual and the GOULD printer manual.
Data input
The input model parameters used in the program are
defined as follows:
MN^= Model number.^Always start with MN = 1
XI^= X co-ordinate of top edge nearest origin
X2^= X co-ordinate of top edge farthest from origin
YI^= Y co-ordinate of top edge nearest origin.
Y2^= Y co-ordinate of top edge farthest from origin
Zl^Depth to top of prism
Z2^= DepLh to base of prism
XN^= X co-ordinate of first observation point
YN^= Y
ZN^= Z
DX^= Station increment along X axis
THETA = Dip of prism edge nearest to origin in degrees
ETA^=^u^farthest from origin in degrees
BETA = Angle between X axis and profile, measured clockwise
from the positive X axis in degrees
DEN^r. Density contrast
NXN^= Number of stations
•
•
•
•
C‘
YesPHI =ETA
Start
/ Read inputdata
PHI =THETA
Yes
calculateFI,F2,F3,F4,F5
-A^'A
M=M4.1
Reset valueof UM
Yes
Change sign
FI,F2,F3,F4,F5
Calculategravity value
SumFl F2 F3F4 F5
Initialise, countersM= IG=0
Correct U(1)for dip
Yes
/ Plot results
/ Plotcross-section
Print resultson
-teletype and
line printer
/ Terminateplot
C St" )
9
Record No 1979/29^0^ Fig. 2 Program flow chart^
G 29-264 A
5.
The program is structured for maximum interactive use by
the interpreter, and may be compiled, loaded, and executed by means
of a system teletype. Model parameters for each case are fed to
the computer using a free-field format.
The source program is stored as a resident disc file
GRAV3S but is also available on paper tape.
Loading the program
To load the program, the following command sequence is
observed:
1. *GF, GRAV3S^This command calls the source program
into the user scratch region.
2. *FT, FL^This command causes the program to be
compiled as a binary relocatable file.
3. *GF, STAT..
^
^This command schedul.es the binary file
for loading.
4. *LD, 0^ This command causes the program to be
loaded.
The above steps are once-only commands and need not be
repeated while the system is up.
Running the program
To run the program, the following command sequence is
observed:
1. *LG, GRAV3^This command causes scheduling of the
program for execution.
2. "MN, X1, X2, Y1,^At this request, type in the appropriate
Y2, Z1, Z2 = "^model parameters.
3. "XN, YN, ZN, DX,^Type in appropriate parameters separated
NXN, DEN, ETA,^by a comma.
THETA, BETA =
4. "MISTAKE IN INPUT^Answer YES or NO. If YES, the program
DATA?"^ will return to step 2.
0
6.
•
•5.^"ANY MORE CASES?"^Answer YES or NO. If YES, the program
will return to step 2 so that additional
cases can be modelled.
The user may log into the program any number of times
using the command *LG, GRAV3.^User commands are preceded by a * as
shown;^terminal replies are given in inverted commas.
An example illustrating the use of the input commands
given in Figure 3.
If more than one case is to be modelled, only the
parameters to be varied need be changed.^For all parameters
preceding those to be changed, type in commas. Following
parameters may be ignored.
Data output
Two modes of data output are utilised. The calculated
gravity values are sent to the user teletype for immediate perusal
(Fig. 3) and also to the line printer for plotting. The graphical
plot includes suitable annotation and a cross-section of the case
modelled (see Figs. 4 and 5). A cross-section of the model is not
produced for oblique profiles.
4. PROGRAM TESTING
The program was tested against Nagy's (1966) formula for
the gravity effect of a right rectangular prism and with one of
Hjelt's (1974) cases.^The results shown in Figure 4 indicate an
excellent fit between the GRAV3 results and the test data.
•
•
•
•
•
40..1F9GPHV=SGFAV:s COPIED TO :CFATCH TRACKS. LENGTH; 201 FECOPD:9 280o MORDC4:*FT9FLTEPO: TERMINAL AI:EMBLY/COMPILATION SYSTEM. BINARY OUTFILE = :TAT2B::*GF.:TAT2B:TAT2B COPIED TO :CPATCH TRACKS, LENGTH: 90 REFORDc9 2800 WORDS:41,LD90
LOADR:LOADLOADF:GRAV3 READYLOADF:SEND
•^::.L139GRAV3GRAV3 ON
MN9:19X29Y19Y2•2192:2=1990.9100.90.9100.95.960.
•
•
XN9YN9ZN. LIX, NX.N9DEN. ETA. THETA. BETA=0.950.90.910.92192.59 45.. 110. 9 O.
MISTAKE IN INPUT DATA?ND
I^MODEL NO.^10^ITRTION^GRAVITY VALUE0 .00 .160 10.00 . 200 20 „ 00 .270 ;0. 000 40 . ciii .490 50.00 .670 4;0.00 . 9400 R0.00 1.89
• 0 90.00 2.20 100.00 2.180 110.00 1.R00 120.00 1.430 17:0.00 1.120 14 0 . 00 86
• 0 150^00 .6A1 ,=.0.00 .50
0 1 7 0 . 0 0 .380 1R0.00 .290 190.00 .220 .o 200. 00 . 17•ANY MORE CASES?
YESETC.ETC.8
Fig.3 Teletype input/output
•
Record No. /979/29 G29-2654_
(x3
CCLEI1 gr.
_ LU
CZ
CC
LO
0x
0
;s
0^ 05r.
0;4.
PMEL^141.
OEWCITr,E1INIFIRDT^2_CHHE
16111DE1^DEPTH^!LH
DIP^1:11461E(EIR)^ITE1.89
SlIP FINCTLE(1TIETR)^HD_ BB
PMIFILE^(IN)^50.513
- PROFILE AMBLE^—LBO —
GRAV 3 values
o Nagy's^values
0
0x 0 1. 0^0
4 0Va
015TANCE(METRE5)".s_as 28_10 58.8121^60.08^MAR^11313.08^1213.811 14E1.1301^168.138^180.18 208_80666
•—•
Lu°'ccr-LU C FISDA - hr TM IT--
F-CLLLIC]:
LIS
43DEL
L.r.1 OFTKIT11TER.DT^TAM
1410EL^DEPTH^18.813CC
HIP^RNELE(ETA)^613_011
STIP ATICELE(THETR)^6H.E10LU 0 4 0 PPr3FILE^ON)^. RB
PRIFILE^/INGLE^BAHCC
0TT. *GRAV 3 values
0
co
-64 0 Hjelt's^values
CECE
0
1.20 A^A 0
0^44.
DISTRNCE(METFlE.S)°:s_as 21.121 411.521^60.88^ 1118.139^1.20.1311 1411.1311^16B.B8^MAO 2E1E813
•
LU"'CC [F-LU
76-'
CLLU.C-D66.
6.6
EIV15';-SETTrin
Record No. 1979/29Fig. 4 Program testing
G29-266A
* 143021^RI. 1
VCEKCITr,r1IITHRZT 2_5888
WIDEL^DEPTH S.88X
DIP^HFIGLE(ET11) 45.88
9IP RP41.8_8(TAE111) 118.88
X P41FI1E^(18) . 58.80
PAIFILE^TINGLE 8.88
C.3-3
Cr
v
cr L"
CtCD
AT 4
DI5TANCE(METRES)28_80^48.80^1.8111^88.88^118.88^128.9H
X
1413.88^1.411.811^188.08^218.118
cassA-ssrtnN
WIDEL. Kl.
t.^X
CER4ITY- TIHTPRZ1 2_4888
1410E1 DEPTH^C_BEI
DIP Atigar,ETA)^4.5.08
PNGLEC1I4E111) 115.88
P41PILE (TM>^SH.88
PilIFILF ANGLE^0_ 88
^*. ^ 4
^
v.^ X
^
X^ *
^* k^ k 0 ..
^
*^ • A
DISTANCE(METRES)
^
28.00^48.10^88.80^811.88^18E1.88^128.138^148.88^!ELBA^1118.88^2911.138
Record No. 1979/29 Fig.5 Examples G29-267A
7.
5.^EXAMPLES
I^ Some further examples of the use of the program GRAV3 are
shown in Figure 5.
6.^REFERENCES
HJELT, S.-E., 1974 - The gravity anomaly of a dipping prism.
Geoexploration, v.12(1), pp.29-39.
• NAGY, D., 19.66 - The gravitational attraction of a right
rectangular prism.^Geophysics, v.31, PP.362-371.
•
•
•
•
•
•
•
•
•
Appendix:^PROGRAM LISTING^ 0
********************U******************************************0******************• **^ ******^ ******
**^ **
• GRAV3^ **x4,^ TERMINALOUTPUT LOGICAL UNIT =
****
-1-1(************34***********************************************************U*********
•
FTN4,B,LPROGRAM GRAV3
• C^AUTHOR- R.D.OGILVY• C:^THI S PROGRAM CALCULATES THE GRAVITY ANOMALY OF A• C^3-DIMENSIONAL DIPPING PRISM, OR TRAPEZOIDAL STRUCTURE.
ALL DIMENSIONS ARE IN METRES• 0^MN=MODEL NUMBERE C^X1=CO-OD OF FIRST TOP EDGE ON X AXIS
X2=CO-OD OF SECOND TOP EDGE ON X AXIS10 C^Y1=00-0D OF FIRST EDGE ON Y AXIS
Y2=C0-OD OF SECOND EDGE ON Y AXIS
^
1471^Z1=DEPTH TO TOP OF PRISM
^
C^Z2 DEPTH TO BASE OF PRISM
^
'L4 C.^XN=X CO-OD OF FIRST FIELD POINT
^
15 C^YN=Y CO-OD OF FIRST FIELD POINT
^
j.■7, C^ZN=Z CO-OD OF FIRST FIELD POINT^1 7,^C.:^12 0^ALL DISTANCES MEASURED IN METRES.
ALL ANGLES MEASURED IN DEGREES_
^
20^DX=STATION INIRFMFNT ALUNG X AXIS▪ C^THETA =DIP OF PRISM(OR TRAPEZOID ) EDGE NEAREST TO ORIGIN_▪ C^ETA=DIP OF PRISM EDGE FURTHEST FROM ORIGIN .
^
23 0^BETA-ANGLE BETWEEN X AXIS AND PROFILE, MEASURED CLOCMISE▪ C^FROM +VE X AXIS
^
OF C^DEN=DENSITY CONSTRAST(
^
2fS C^c1C=AFAJ I TAT I 'NiL CONSTANT (C .G S)
^
27 r^HXN=NUMBER OF STATIONS
^
RS C.^AG=ARRAY FOR GRAVITY VALUES
^
C^STAT=ARRAY FOR OBSERVATION POINTS30 r.31^DIMENSION AG(400),STAT(400),F1(2),F2(2),F3(8),E4(2)1U(S)
DIMENSION F5(8),U(2).V(2),W(2)
^
33^INTEGER MN,NXN
^
34^REAL X1,X2,Y1,Y2,21,Z2,XN,YN,ZN,DX,DEN,ETA,THETA,BETO
^
35^INTEGER STR1(10).STR2(7),STR3(3),STR4(S),STR5(11),
^
36^*STR6(8STR7(8STR8(2),STR10(7STR11(7),STR9()DATA STR1/2HGR,2HAV,2HIT.2HY .2HVA,2HLU,2HE(,2HMG,2HAL,2HS)/'
^
32^DATA STR2/2HDE.2HPT,2HH(.2HME,2HTR,2HES.2H) /
^
39^DATA STR3/2HDI,21-1ST,2HAN,2HCE,2H(M,2HET.2HRE.2HS)/
^
40^DATA STR4/2HM0,2HDE.2HL .2HNO.2H. ,RH ,OH ,2H
^
41^DATA STR5/2HDE,2MNS,2HIT,2HY ,2HCO,2HNT.RHRA,ZHST,2H ,2H .2H
^
42^DATA STR8/2HMO,2HDE,2HL .2HDE,2HPT,2HH^.2H
^
43^DATA STR7/2HDI.2HP ,2HAN,2HGL,2HE(.2HET,2HA) . ,RH
^
44^DATA STR8/2HDI,2HP ,2HAN,2HGL,2HE(,2HTH,2HET,RHA)/
^
45^DATA STR9/2HPR,2HOE.2HIL.2HE .2H(Y,2HN)/
^
46^DATA STR10/2HPR.2HOF,2HIL.2HE ,2HAN,2HGL:2HE
^
47^DATA STR11/2HCR,2HOS,2HS-,2HSE.2HCT.2H10.2MN /48
^
49^READ INPUT DATASO r
^51^CALL RMPAR(LU)
^
52^A WRITE(LU.300)
^
53^300 FORMAT(/2X,"MN.X1.X2,Y1,Y2,Z1,,Z2=")
^
54^READ(LUAOMN.X1,X2,Y1,Y2,7.1,Z2
•
55565758596e
WRITE(LU,301)301 FORMAT(/2X,"XN,YN,ZN,DX,NXN.DEN,ETA,THETA,BETA=")
READ(LU,*)XN.YN.ZN.DX.NXN,DEN,ETA,THETA,BETA14 1JRITE(LU,303)
303 FORMAT(/2X,"MISTAKE IN INPUT DATA?")READ(LU,6)NGOOD• 61 6 FORMAT(A2)
62 IF(NGOOD.E0.2HYE)G0 TO 163 r64 C CONVERT INPUT DATA65 C66 GC=6 67/10000000067 pi=3.14159
40 68 ETA=ETA*PI/130THETH=THETA*PI/180
70 BETA=BETA*Pis12071 •,<G=:-:s472 C72 nn 9 1 L=1 NXN74 'LtDX*COS(RETA)+XN
40 75 Y=(i_^i•tDX:CSIN(BETA)+YN76 STPrL^-11*flX
H=Z2-.2179 U(1)=X-X279 0(2)=X-X180 Vii)=Y-Y221 V(2)=Y-Y122 t.j(1;=7H-7233 W(2)=ZN-2184 CRC C CALaji ATE GRAVITY EUNCTION G2.6 r27 M=1
40 82 G=089 no^10^1=1,2
90 DO 10 J=1.291 DO 10 K=1.292 1F.(AEL..i^-1.001^LT.0)1A(K)=0^001Cr? IF(i^EO^1)PHI=ETO94 117(1^E0.2)PHI=THETA
40 IFW FO^1) 13(1)=U(I :-H/TON(PHI)96 R==;OPT(U(I)*U(I)+V(WiN(j)+W(K)*W(K))
P=1..“II-W(K)/TAN(PHI)98 IFABS(P)-0 001) LT 0)P=0.00199 0=w(K)+U(1)/TAN(PHI)100 71(M)=WW)*ATAN((V(J)*U(U)/(WOO*P))• 101 F2(M)=-P*SIN(PHI)*COS(PHI)*ATANO(V':J)*0)/(P*P))1 02 F200=-P,W=zIN(PHI)*c1H(PHI)*A1 nG(V(J)+R)103 F4(M)=-V(J)*A! OG(U(I)+R)104 FE(H)=VJ)*COSCPHI)*ALOG(0*SIN(PHI)+R)10510% C. 4.0R^IjK E0 := , )G0 TO^19107 S F1(M)=-F1(M)
40 108 F8(0)=-F2(M)109 F2(1)=-F2(M)
9-
110 F4(M)=-F4(M)^.111 F5(M)=-F5(M)112 19^IF(K.E0.1)U(1)=U(1)+H/TAN(PHI)113 M=M+1114 10 CONTINUE115 DO 11 N=1,8116 G=G+F1(N)+F2(N)+F3(N)+F4(N)+F5(N)117 11 CONTINUE118 C119 C CALCULATION OF GRAVITY VALUE120 C121 AG(L)=-100000.0*GC*DEN*G122 99 CONTINUE123 XN=XG124 C125 C PRINT RESULTS126 C127 WRITE(LU,3)MN128 r WRITE(6.,3)MN129 3 FORMAT(1H1;7X,9HMODEL NO .110)130 1RITE(LU,202)131 C WRITE(6,202)132 202 FORMAT(1H0.7X.7HSTATION,10X,13HGRAVITY VALUE)133 DO 56 J=1,NXN134 WRITE(LU,60)STAT(U),AG(J)135 C WRITE(6.60)STAT(J),AG(U)136 60 FORMAT(1H0,5X,F10 2,GX,F10.2)137 Si; CONTINUE133 C139 C PLOT AXIS140 C141 DIST=DX*FLOAT(NXN)/10.142 SI2=-Z2/3.143 CALL PLOTS(17-10 .0)144 CALL FACTR(0.5)145 IF(MN.E0.1)CALL PLOT(1.,0.5,-3)146 CALL AXIS(0..4—STR1.20,5-90-0-0.5)147 CALL AXIS(0^,0.,STR2,14,3.,90.,Z2,S12)148 CALL AXIS(0..3^.STR3,16,10-0..XG,DIST)149 C150 C PLOT POINTS151 C152 CALL PLOT(0.,4.,-3)153 XP=0.154 DO 600 I=1,NXN155 YP=AG(I)/SCM156 CALL SYMB(XP,YP,0.1,7,0.,-1.0.1)157 XP=XP+DX/nIc7158 600 CONTINUE159 BETA=BETA*130./PI.160 IF(IFIX(DETA).GT.0)G0 TO 900161, XP1=X1/DIST-XG/DIST162 YP1=Z1/5I2163 XP2=X2/DIST-XG/DIST164 • XP3=(X2+H/TAN(ETA))/DIST-XG/DIST
-09
166^XP4=(X1+H:TAN(THETA))/DIST-XG/DIST166^CALL PLOT(0.,-1.,-2.)167^CALL PLOT(X.P1.YP1,3)168^CALL PLOT(XP2,YP1.2)169^CALL PLOT(XP3,-3-2)170 .^CALL PLOT .(XP4,-'3 .-
171^CALL PLOT(XP1,YP1,2)172^CALL SYMB(7.,-1.5,0.1,STR11,0-13)173^900 THETA=THETA*180./PI174^ETA=ETA*180../P1175^CALL SYMB(7-5.5.0.1,STR4,0-16)176^CALL SYM8(7-5-0.1,STR5,0-22)177^CALL SYMB(7-4.7.0.1,STR6,0-16)178^CALL SYMB(7-4.4,0.1,STR7,0-16)179^.CALL SYM8(7-4.1,0.1,STR8,0.1,16)180^CALL 5YMB(7-.3.8.0.1.STR9,0-12)181^CALL SYMB(7-3.5,0.1.STR10,0-14)182^CALL NUMB(8.3.5.1,FLOAT(MN),0-0)
. 183^CALLNUMB(8.8,5.0,0.1,DFN:0-4)184^CALL NUM9(8.8,4.7,0.1 .:21,0-2)1E5^CALL NUME(8.8.4.4.0.1.ETA,0-2)186^CALL NUM8(8.8,4.1,0.1,THETA,0-2)187^CALL NUMB(8.8,3.3,0.1,YN.0-2)188^CALL NUMB(8.8.3.5,0.1.BETA,0-2)189 C190 C^TERMINATE PLOT191 r192^27 CALL PLOT(0. - .0 .999)
193^CALL GOPLT194^75 JRITE(LU..2O)195^20 FORMAT(/2"ANY MORE CASES?")196^RFADO 13, -*))Mr1RF197^30 FORMAT(A2)198^IF(MORE.E0.2WE)1 2719';^STOP200^END201^ENDS